Dynamic models of Wasserstein-1-type unbalanced transport
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 23.

We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which transport costs are proportional to transport distance. For those models we derive an equivalent, computationally more efficient static formulation, we perform a detailed analysis of the model optimizers and the associated optimal mass change and transport, and we examine which static models are generated by a corresponding equivalent dynamic one. Alongside we discuss thoroughly how the employed model formulations relate to other formulations found in the literature.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018017
Classification : 49K15, 37N40
Mots-clés : Wasserstein distance, unbalanced transport, convex optimization
Schmitzer, Bernhard 1 ; Wirth, Benedikt 1

1 
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Schmitzer, Bernhard; Wirth, Benedikt. Dynamic models of Wasserstein-1-type unbalanced transport. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 23. doi : 10.1051/cocv/2018017. http://www.numdam.org/articles/10.1051/cocv/2018017/

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